Advanced Math
4.2-4.3 Exponential Functions & Logs
Name__________________________________
April 2014
1. Name the two types of exponential functions and give an example of each type.
Type 1: __________________ Example__________________
Type 2: __________________ Example__________________
Determine which of the following functions are exponential growth and which are exponential decay. Circle
your answer.
2.
𝑦 = 0.2𝑥
GROWTH DECAY
3.
𝑦 = 4𝑥
4.
GROWTH DECAY
𝑦 = 6(0.5)𝑥
GROWTH DECAY
5.
𝐴 = 1000(1.25)𝑥
GROWTH DECAY
Graph the given exponential function using the following domain for 𝒙 : [−𝟐, 𝟐]. State whether the graph shows
exponential growth or decay.
1𝑥
6. 𝑦 = 3𝑥
7. 𝑦 = 3
Rewrite each equation in its exponential form.
8. log 10,000= 4
9. log4 0.25= -1
11. ln𝑒 2 = 2
1
12. log6 216= −3
Rewrite each equation in its logarithmic form.
14. 45 = 1024
15. 360.5 = 6
17. 36 = 729
1
18. 4-5 = 1024
10. log8 512= 3
1
13. log2 64= −6
16. 73 = 343
1
19. 3-4 = 81
Solve.
20. logx 2 = ½
1
23. log 2 32 = x
1
21. log8 512= x
22. log4 64= x
24. log2 64= x
25. ln 𝑒 4 = x
For the following application problems, show the equation (if one hasn’t already been given to you) and show the
substitution of all the variables necessary to solve. Points will be given on the quiz for this work!
26.
The attendance for a basketball team declined at a rate of 5% per game throughout the losing season. The
attendance can be approximated using the formula A(g) = 23,000(.95)g where g is the number of games since the
first game. Find the attendance at the 15th home game (g = 14) if 23,000 people were at the first game.
26.)________________
27.
The number of pay phones in use in the U.S. has been declining due (large in part) to an increased usage of cell
phones. The function 𝐴 = 2.28(0.9)𝑥 can be used to model the number of pay phones (in millions) 𝑥 years
since 1999.
a.
b.
According to this equation, how many pay phones were there
in the U.S. in 1999?
27a.)_______________
How many pay phones were there in the U.S. in 2005?
27b.)_______________
28.
Kristin starts an experiment with 7500 bacteria cells. The formula A = 7,500(1.32)t can be used to approximate
the number of bacteria cells after t hours. How many bacteria cells can be expected in the sample after 12
hours?
28.)_______________
29.
An investment pays 4.2% interest compounded monthly. If $25,000 is invested in the account, what will be
the balance after 15 years?
29.)________________
30.
A college savings account pays 7.2% interest compounded continuously. What is the balance of an account after
18 years if $21,000 was initially deposited?
30.)________________
31.
32.
In 2003, Lucy received $10,000 from her grandmother. Her parents invested it in an account that earns 4.4%
interest annually.
a.
What would be the balance of the account in 2025?
31a.)_______________
b.
If Lucy’s parents decide to invest the money in an account where the
interest is compounded monthly, how much more money will be in
the account in 2025?
31b.)_______________
Find the balance of an account after 20 years with 1.2% interest compounded twice a month. The account is
opened with $100.
32.)________________
33.
An investment pays 6.3% interest compounded continuously. If $5,000 is invested in the account, what will be
the balance after 12 years?
33.)________________
34.
The student population at Grosse Pointe South is approximately 1700. If enrollment increases
approximately 1.5% each year, the population can be approximated using the formula
P(t) = 1,700(1.015)t . How many students will attend South in 5 years?
34.)______________
35.
The Miller’s bought a condominium for $18,500. Assuming that the value of the condo will
Grow each year, the following equation can be used to determine the worth of the condo:
C(t) = 18,500(1.05)t. How much will the condo be worth in 7 years?
35.)______________
36.
You buy a commemorative coin for $25, whose value increases each year. The equation A = 25(1.035)t
approximates the coin’s value after t years. How much will the coin be worth in 15 years?
36.)______________
37.
You’re off to college! You buy a computer for $2500. The value of the computer can be modeled by the
equation V(t) = 2500(.8)t. What will be the value of the computer in 2 years?
37.)______________
38.
A cup of coffee contains 130 milligrams of caffeine. Since caffeine is eliminated from the body each hour, the
amount of caffeine remaining in your body is approximated by the equation C(t) = 130(.89)t where t is measured
in hours. How much caffeine will still be in a person’s body in 6 hours?
38.)______________
39.
Suppose you deposit $1200 in an account paying 3.5% interest compounded continuously.
How much will be in the account after 7 years?
39.)______________
40.
The population of Buffalo, New York, declined and can be approximated by the equation
P(t) = 465, 900(.983)t where t is years since 1970.
Use the model to predict Buffalo’s population in 2000.
40.)_____________
41. Freedom National Bank offers several types of savings accounts with different interest rates and compounding
periods.
Money-Market Account: Pays 3.8% interest, compounded quarterly.
Standard Savings Account: Earns 3.55% interest compounded monthly.
All-in-One Account pays 3.2% interest compounded continuously.
You have $2000 to deposit. Which account is the best investment for your money?
a) First make a guess.
__________________________
b) Now compare the balance in each account after 25 years. Show your work in the table below.
Based on your work, which plan is best?
_________________________
Money Market Account
Standard Savings Account
All-in-One Account
Answers:
1.
Growth; Decay
2. D
3. G
4. D
5. G
6 & 7. See graphs
8. 104 = 10,000
9. 4-1 = 0.25
10. 83 = 512
11. e2 = e2
13. 2-6 = 1/64
14. log4 1024= 5
15. log36 6= ½
16. log7 343= 3
12.
6-3 = 1/216
1
1
17. log3 729= 6
18. log4 1024= -5
19. log3 81= -4
20. 4
21. 3
22. -3
23. -5
24. 6
25. 4
26. 11,217 ppl
27. 2.28million; 1.21million
28. 209,869 cells
29. $46,888.66
30. $76,747.62
31. $25,787.60; $492.57
32. $127.11
33. $10,648.70
34. 1831 students
35. $26,031.36
36. $41.88
37. $1,600
38. 64.61mg
39. $1,533.15
40. 278,547
41. Money Market Acct.